Introduction to mathematical analysis
The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, the Lebesgue integral, vector calculus and differential equations. After having created a solid foundation of topolog...
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| Главные авторы: | , |
|---|---|
| Формат: | Livre numérique |
| Язык: | Anglais |
| Опубликовано: |
Basel :
Springer Basel : Springer e-books : Imprint: Birkhäuser : Springer e-books
[20..].
Cham : Springer Nature |
| Предметы: | |
| Online-ссылка: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Примечание: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Introduction to mathematical analysis, Igor Kriz, Aleš Pultr, 2013, Basel, Birkhäuser, 1 vol. (XX-510 p.), 978-3-0348-0635-0 |
Оглавление:
- contient aussi des exercices
- Preface
- Introduction
- Part 1. A Rigorous Approach to Advanced Calculus
- 1. Preliminaries
- 2. Metric and Topological Spaces I
- 3. Multivariable Differential Calculus
- 4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral
- 5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration
- 6. Systems of Ordinary Differential Equations
- 7. System of Linear Differential Equations
- 8. Line Integrals and Green's Theorem
- Part 2. Analysis and Geometry
- 9. An Introduction to Complex Analysis
- 10. Metric and Topological Spaces II
- 11. Multilinear Algebra
- 12. Smooth Manifolds, Differential Forms and Stokes' Theorem
- 13. Calculus of Variations and the Geodesic Equation
- 14. Tensor Calculus and Riemannian Geometry
- 15. Hilbert Spaces I: Definitions and Basic Properties
- 16. Hilbert Spaces II: Examples and Applications
- Appendix A. Linear Algebra I: Vector Spaces
- Appendix B. Linear Algebra II: More about Matrices
- Bibliography
- Index of Symbols
- Index.